Linearization of some Poisson-Lie tensor
type: Item
instance of: scholarly article
title: Linearization of some Poisson-Lie tensor
zbMATH Open document ID: 0888.22006
DOI: 10.1016/S0393-0440(97)00004-1
author: V. Chloup-Arnould
published in: Journal of Geometry and Physics
publication date: 1998-02-04T00:00:00Z
review text: Linearization problems for Poisson-Lie (P.-L.) tensors (Weinstein, 1983; Conn, 1984; Dufour, 1990; Molinier, 1993) are considered. The existing bijection between P.-L. structures on a connected, simply-connected Lie group \(G\) and the bialgebra structures \((g,g^*)\) on the Lie algebra \(g\) and its dual mapping \(g^*\) of \(G\) (Drinfeld, 1983) is used as starting point. It is shown that any P.-L. tensor \(P\) on \(G\) such that the linear approximation \(g^*\) is reductive is analytically reducible. Some results on P.-L. structures whose linear approximations are direct sums with a semisimple factor are also presented. Finally, some examples of linearizable and nonlinearizable exact P.-L. structures on some nilpotent groups are given.
reviewed by: A. A. Bogush
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 1112274
zbMATH Keywords: Poisson-Lie structures
zbMATH Keywords: Lie group
zbMATH Keywords: bialgebra structures
zbMATH Keywords: Lie algebra
zbMATH Keywords: dual mapping
zbMATH Keywords: nilpotent groups
MaRDI profile type: Publication
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cites work: Q3040173
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cites work: Cohomology of Lie algebras
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description: scientific article; zbMATH DE number 1112274